y^{''}+5y^'-2y=0,y(0)=5,y^'(0)=-5

Lösung

y^{^{''}} + 5 y^{^{'}} - 2 y = 0, y (0) = 5, y^{^{'}} (0) = - 5

y = (5 - \frac{5 33 - 15}{2 33}) e^{\frac{( - 5 + 33 ) t}{2}} + \frac{5 33 - 15}{2 33} e^{\frac{( - 5 - 33 ) t}{2}}

Schritte zur Lösung

y^{''} (t) + 5 y^{'} (t) - 2 y = 0

Solve linear ODE:

y = (5 - \frac{5 33 - 15}{2 33}) e^{\frac{( - 5 + 33 ) t}{2}} + \frac{5 33 - 15}{2 33} e^{\frac{( - 5 - 33 ) t}{2}}

y = (5 - \frac{5 33 - 15}{2 33}) e^{\frac{( - 5 + 33 ) t}{2}} + \frac{5 33 - 15}{2 33} e^{\frac{( - 5 - 33 ) t}{2}}

3 y^{^{''}} + 4 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = - 1

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{'''}} + y^{^{''}} - 6 y^{^{'}} + 4 y = 0

y^{^{''}} + 2 y + y = 0, y (0) = x e^{- x}

y^{^{''}} - 6 y^{^{'}} + 2 y = 0